Approximate method for radiative transfer in scattering absorbing plane-parallel media.

An approximate method of solution is developed for calculating the specific intensities in scattering and absorbing plane-parallel media under an unpolarized unidirectional incident radiation. In this method, the phase function for a single scattering is represented by a Legendre series; the scattered intensity is represented by a series consisting of intensities representing the different orders of scattering. In this manner, the original integral-differential transfer equation is reduced to a system of ordinary differential equations for intensities representing various scattering orders. A simple numerical integration in optical depth is all that is necessary to obtain a solution. In the case of isotropic scattering, solutions are given in closed form. The present approximate solutions are compared with exact numerical ones for both the isotropic and anisotropic cases and are found to agree within 10-25%, which is adequate for most engineering applications.